The present invention relates to a digital signal timing synchronization process. It is used in radio transmission systems and more particularly in code distribution multiple access (CDMA) systems.
The principles of a digital communication and the link existing between baseband signals and carrier frequency signals are known and described e.g. in the work by John G. PROAKIS entitled xe2x80x9cDigital Communicationsxe2x80x9d, McGraw Hill International Editions.
FIG. 1 is the circuit diagram of a radio digital transmission chain.
In the transmission chain E, an original digital signal 10A which it is wished to transmit undergoes a preprocessing in a circuit 10. This preprocessing can involve numerous scrambling, interleaving or coding operations, which will not be dealt with in the remainder of the description. The circuit 10 delivers a sequence 10B of digital signals a(k), in which k designates the rank of the symbol. The symbol a(k) is in general a complex number represented by a pair of real values. The frequency of the symbols a(k) is designated Hs and the corresponding period Ts, with Ts=1/Hs.
On the basis of the sequence a(k), a shaping device 20 develops the baseband analog signal 20A to be transmitted and designated b(t), in which t is the time variable. The signal b(t) is a complex signal represented by two real quadrature signals bI(t) and bQ(t). The baseband signal 20A is converted to a carrier frequency by a radio transmitter 30, which incorporates various means, namely a modulator, frequency conversions, filters, local oscillators, amplifiers and an antenna, but to which no further reference will be made hereinafter. It is merely assumed that the transmitter performs a linear, mathematical operation with respect to the baseband signal. The transmitted radio signal 30A is propagated to the receiver, whilst undergoing different types of degradations.
In the reception chain R, the radio signal received 40A is firstly processed by a radio receiver 40, which incorporates different devices, namely an antenna, frequency conversion means, filters, local oscillators and amplifiers, but to which no further reference will be made hereinafter. The receiver 40 delivers an analog baseband signal 40B, which is designated r(t). The signal r(t) is a complex signal represented by two real quadrature signals rI(t) and rQ(t). On the basis of the signal r(t) a detection device 50 develops a set of symbols or digital samples 50A. The set of detected samples 50A constitutes a more or less faithful image of the sequence of symbols a(k). The detected samples 50A undergo a postprocessing in a circuit 60. This postprocessing comprises various operations corresponding to the preprocessing operations 10 of the transmission chain E and delivers the restored signal 60A.
The development of the set of detected samples 50A assumes as precisely known the value of the period Ts of the timing of the sequence a(k) and its phase relative to the baseband signal r(t). A synchronization device 70, by means of the signals 50B which it exchanges with the detection device 50, estimates the timing of the signals received and communicates the result of this estimate to the detection device. Certain detection processes known as coherent demodulation also require the knowledge of the phase of the carrier frequency of the radio signals received. This knowledge is not envisaged here and demodulation can be both coherent and non-coherent. It is merely assumed that the beat frequency between the carrier frequency used in the receiver and the real carrier frequency is low compared with the timing Hs of the symbols a(k).
The functional partitioning which has been made is to a certain extent arbitrary and certain operations can overlap. However, it is assumed that there is effectively a received baseband signal 40B or an equivalent representation of this signal in the form of digital samples.
The present invention essentially relates to the synchronization operation carried out in the reception chain.
Synchronization is linked with the shaping of the baseband signal to be transmitted b(t) and to the corresponding detection conditions. It is here assumed that the shaping corresponds to the linear mathematical operation:       b    ⁡          (      t      )        =            ∑      k        ⁢          xe2x80x83        ⁢                  a        ⁡                  (          k          )                    ·              h        ⁡                  (                      t            -            kTs                    )                    
in which   ∑  k
represents a summation on all the symbols a(k) and in which h(t) designates a real or complex function of the time t.
An important case is that of the direct sequence spreading, where       h    ⁡          (      t      )        =            ∑              n        =        0                    N        -        1              ⁢          xe2x80x83        ⁢                  α        ⁡                  (          n          )                    ·                        g          ⁡                      (                          t              -              nTc                        )                          .            
In this expression, xe2x88x9d(n) is a family of previously defined, complex or real numbers independent of the value of the symbols a(k) which it is wished to transmit. The numbers xe2x88x9d(n) are known as chips in terminology widely used in this field. With each rank k are associated N successive chips xe2x88x9d(n) numbered n=0 to n=Nxe2x88x921. The chips are delivered with a period Tc=Ts/N and the corresponding timing is designated Hc. The number N of chips per symbol is called the spread factor. The function g(t) is a real or complex function independent of the rank k and the number n. It is called the xe2x80x9cshaping functionxe2x80x9d of the chip. The direct sequence spread CDMA transmission systems allocate to each user a particular family of chips xe2x88x9d(n), the different families of chips being chosen so as to reduce interference between users.
Although the invention does not apply directly to the actual detection, it is necessary to take account thereof. In the case of a transmission channel which does not deform the signal, but merely superimposes thereon an independent interference signal called Gaussian white noise, the optimum detection is obtained by the matched filtering method or an equivalent method. This method consists of applying the baseband signal received r(t) to a transfer function filter h*(xe2x88x92t) in order to obtain a signal s(t):
s(t)=h*(xe2x88x92t)*r(t)
where * represents the complex conjugation operation when it is placed at the exponent, or the convolution operation when it is placed at midheight. Strictly speaking, matched filtering is carried out with the aid of a transfer function filter h*(Trxe2x88x92t), where Tr is a fixed delay or lag chosen in such a way that the function h*(Trxe2x88x92t) is causal with respect to the variable t. This delay corresponds to the time necessary to complete the calculation of s(t) on the basis of r(t) for a given time t, but plays no part in the following explanations. For reasons of simplicity, it is assumed to be zero hereinafter. The values of the signal s(t) at appropriately chosen times constitute the set of detected samples 50A or would make it possible to develop said set with the aid of supplementary operations.
In the case of direct sequence spreading, matched filtering is broken down into a filtering matched to the shape of the chip:
sc(t)=g*(xe2x88x92t)*r(t)
and a filtering matched to the chip sequence:       s    ⁡          (      t      )        =            ∑              n        =        0                    N        -        1              ⁢          xe2x80x83        ⁢          α      *                        (          n          )                ·                              s            c                    ⁡                      (                          t              +              nTc                        )                              
where the function sc(t) is used as a calculation intermediate. Filtering matched to the chip sequence is called despreading.
Numerous methods exist for the recovery of the timing or clock on the basis of the baseband output signal of the matched filter. Certain make use of a global approach where the carrier frequency phase, timing phase and symbols are jointly estimated. From the practical standpoint it is often simpler to separately estimate the phase of the timing or clock. In general terms, timing recovery requires a derivation with respect to the time of the baseband output signal of the matched filter, in order to reveal signal transitions. Among possible processes, certain bring together a differentiator and a phase locked loop, whereas others effect a non-linear operation followed by a filtering and a zero passage detector of the signal, whilst still others multiply the signal with itself in delayed form.
In reality, the radio signal is often propagated in a complex manner between the transmitter and the receiver following several different paths. This applies with respect to the earth radio mobile channel. The signal received is presented to the receiver at delayed times. Optimum detection must take account of the pulse response of the channel. From the mathematical standpoint, filtering matched to the pulse response of the channel implements a recombination of all the existing paths. This operation is partly performed in conventional rake receivers, which combine a limited number of paths. The number of elementary timing recovery devices is of the same level as the number of processed propagation paths.
The aim of the invention is to implement a common timing recovery process able to keep pace with a very large number of paths.
In the case of an ideal, noise-free transmission, the received baseband signal r(t) is linked with the baseband signal to be transmitted b(t) by an expression of form:
r(t)=A.exp(jxcfx86).b(txe2x88x92xcfx84)
where j designates the imaginary part of a complex number (j2=xe2x88x921) and exp is the exponential function, A and xcfx86 respectively represent the amplitude and phase of the gain of the transmission channel and xcfx84 is the propagation time. If the carrier frequency is not precisely known, the phase term xcfx86 evolves slowly during time. This term is cancelled out or compensated in the case of a coherent demodulation. The output signal s(t) of the matched filter is of form:       s    ⁡          (      t      )        =      A    ·          exp      ⁡              (                  j          ⁢                      xe2x80x83                    ⁢          ϕ                )              ·                  ∑        k            ⁢                        a          ⁡                      (            k            )                          ·                  Rh          ⁡                      (                          t              -              τ              -              kTs                        )                              
in which Rh(t) designates the time autocorrelation function of h(t). Generally the function h(t) is chosen in such a way that its autocorrelation Rh(t) verifies the so-called Nyquist condition:
Rh(nTs)=0
for any integer n differing from zero and assumes low values as soon as the variable t assumes values higher than a few symbol periods Ts. Under these conditions, the value of s(t) at the time xcfx84+nTs is:
s(xcfx84+nTs)=A.exp(jxcfx86).a(n).Rh(0)
and its value at a time xcex8+xcfx84+nTs, where the quantity xcex8 is small compared with Ts, is approximately:
xe2x80x83s(xcex8+xcfx84+nTs)≅A.exp(jxcfx86).a(n).Rh(xcex8)
The square of the modulus of the quantity s(xcex8+xcfx84+nTs) is:
|s(xcex8+xcfx84+nTs)|2≅A2.|a(n)|2.|Rh(xcex8)|2
If there is interest in the case of a digital modulation by phase displacement, the value of |a(n)|2 is then independent of the transmitted symbol and the quantity |s(0+xcfx84+nTs)|2 is approximately proportional to |Rh(0)|2. The autocorrelation function Rh(t) takes on its maximum value at t=0. If the function h(t) is carefully chosen, the autocorrelation function Rh(t) has a narrow main peak in the vicinity of t=0 and possibly very attenuated secondary maxima when the value of t increases. Thus, the observation of the position of the successive maxima of |s(t)|2 makes it possible to locate the time xcfx84+nTs and therefore recover the timing. Hereinafter, the quantity |s(t)|2 will be called the power of the signal after matched filtering.
In the case of a multipath transmission there is no single propagation time and, on the evolution of the power |s(t)|2 in time, there are packets of successive peaks in the vicinity of the mean position of each symbol a(k). Each correlation peak corresponds to a particular propagation path and each packet of peaks occupies a time interval corresponding to the difference between the longest propagation time and the shortest time. Such a time interval is called a xe2x80x9cpath windowxe2x80x9d. The synchronization process proposed by the invention consists of placing a window on the packets of correlation peaks. The centre of the window then defines a mean propagation time xcfx84 and the position of the different paths is referenced with respect to said time.
The received baseband signal r(t) delivered by the radio receiver has undergone a low pass filtering. Therefore there is an upward limitation to its frequency spectrum. The same applies with respect to the shaping function h(t). Consequently the signal s(t) is also frequency-limited. From the mathematical standpoint, if Fmax designates the highest frequency contained in the spectra of functions r(t), h(t) and s(t), these functions are exactly represented by their samples r(mTe), h(mTe) and s(mTe) taken at times mTe regularly spaced by a quantity Te, known as the sampling period, provided that said quantity verifies the so-called Shannon condition:   Te   less than       1                  2        ·        F            ⁢              xe2x80x83            ⁢      max      
It is possible to choose here as the sampling period Te a submultiple of the symbol period Ts:   Te  =      Ts    M  
in which M is an integer higher than 1 and compatible with the Shannon condition. It is not indispensable to choose Te as a submultiple of Ts, but it is indispensable that the choice of M is compatible with the Shannon condition. The samples of s(t) are expressed with the aid of samples of r(t) and h(t):       s    ⁡          (      mTe      )        =      Te    ·                  ∑        i            ⁢              h        *                              (            iTe            )                    ·                      r            ⁡                          [                                                (                                      i                    +                    m                                    )                                ·                Te                            ]                                          
For ease working takes place with the quantity:
y(m)=s(mTe)/Te
because the factor Te plays no part. From the practical standpoint, the function h(t) assumes low values on the basis of a certain value of t and it is possible to limit the summation on i to an interval between two relative integers i1 and i2 a priori chosen in accordance with the decrease of h(t):       y    ⁡          (      m      )        =            ∑              i        =                  i          1                            i        2              ⁢          xe2x80x83        ⁢          h      *                        (          iTe          )                ·                  r          ⁡                      [                                          (                                  i                  +                  m                                )                            ·              Te                        ]                              
The successive samples y(m0), y(m0+1), . . . , y(m0+Nexe2x88x921), where m0 is a particular rank and Ne a given positive integer, are located in a window of initial time m0Te and width NeTe. The integer Ne is obviously chosen as a function of the dispersion of the paths. As a symbol period Ts contains M sampling periods Te, it is possible to represent the sampling rank m in the form:
m=M.p+q
in which p and q are relative integers. For a given integer q0, when q assumes the values of q0 to q0+Nexe2x88x921 and p assumes all possible integral values, a window of width NeTe is obtained, which is reproduced with the period Ts.
The synchronization process according to the invention is based on the one hand on the calculation of the total power in the window:       ∑          m      =              m        0                            m        0            +      Ne      -      1        ⁢      xe2x80x83    ⁢            "LeftBracketingBar"              y        ⁡                  (          m          )                    "RightBracketingBar"        2  
and on the other on the distribution of powers |y(m)|2 within the window.
Synchronization involves two modes, namely an acquisition mode and a tracking mode. In the acquisition mode, the M possible positions, for q=0 at Mxe2x88x921, of the periodic window [Mp+q;Mp+q+Nexe2x88x921] are successively examined and the total power P(p,q) in each window is calculated:       P    ⁡          (              p        ,        q            )        =            ∑              i        =        0                    Ne        -        1              ⁢          xe2x80x83        ⁢                  "LeftBracketingBar"                  y          ⁡                      (                          Mp              +              q              +              i                        )                          "RightBracketingBar"            2      
This power is higher when there are paths in the window than when there are no paths. At the moment where the total power assumes its maximum value, the rank q has a certain value q0 and the window is approximately set on the packet of paths.
There is then a passage to the tracking mode. With each rank i within the window is associated a significance c(i) as a function of its position with respect to the centre of the window. This significance is a monotonic function (in the broadest sense) of the rack i. The sum of the weighted powers:       ∑          i      =      0              Ne      -      1        ⁢            c      ⁡              (        i        )              ·                  "LeftBracketingBar"                  y          ⁡                      (                          Mp              +                              q                0                            +              i                        )                          "RightBracketingBar"            2      
indicates where the mean power of the packet of paths is located with respect to the centre of the window and can be used for correcting the sampling time, thereby locking the position of the window on the packet.
Specifically, the present invention consequently relates to a digital signal timing synchronization process, in which sampling takes place with a certain sampling period of an analog signal resulting from the transmission of a signal modulated with the aid of a shaping function, a matched filtering of the samples takes place, said filtering being matched to the shaping function used by the modulation and leading to correlation samples, said process being characterized in that:
the elementary power of each correlation sample is calculated,
a sliding window of width Ne times the sampling period is defined, i.e. NeTe and commencing at a certain rank,
for each sliding window a calculation takes place of the sum of the elementary powers of the correlation samples located in said window for one symbol and for a given number of symbols,
the window for which the sum of the powers is at a maximum is determined,
the synchronization is then defined by the position of the synchronized window on the window with the maximum power sum, and by the rank of each correlation sample within said window.
Preferably, two types of operation are performed and working occurs in two modes:
a) in a first type of operations, known as scanning operations, there is a successive examination of all the possible positions of the sliding window (so-called scanning cycle) and for each position a calculation takes place of the global power (Pa) of the correlation samples (y(m)) contained in the sliding window, there is an identification of the window for which the global power is highest since the start of the cycle and up to the present position and the value of said highest power (Pam) is stored,
b) in a second type of operations, called tracking operations, account is taken only of the correlation samples (z(m)), whose rank is in a so-called tracking window, calculation taking place on the one hand of the global power (Pb) of said samples and on the other of a signal (d) making it possible to lock the centre of said window on the mean position of the elementary powers which it contains,
c) in a first operating mode known as the acquisition mode,
on the one hand on each occasion where in a sliding window appears a global power (Pa) higher than the last power (Pam) stored since the start of the scanning cycle and up to the present position, to the tracking window is allocated the present position of the sliding window and a verification process is initiated,
on the other hand when the scanning cycle is ended, there is a passage into a tracking mode,
d) in a second operating mode, known as the tracking mode,
on the one hand the transfer mechanism of the position of the sliding window to the tracking window is inhibited,
on the other hand when the permanent verification fails there is a return to the acquisition mode.